We visualize the Hopf bundle S1 -> S3 -> S2 by means of the stereographics projection S3 -> R3. Furthermore, we visualize the Dirac connection on this Hopf bundle. The horizontal lifts of a curve form the base space S2 to a total space S3, with respect to this connection, and are calculated and visualized. This is done as an appendix of the author's PhD thesis. The main part of the thesis shows different aspects of self-duality that can be seen as generalizations of the Dirac connection.